Physics

Physics

Problem

State the expression for the instantaneous emf produced by a generator coil of NN turns and area AA rotating with constant angular speed ω\omega in a uniform magnetic field BB, when the plane of the coil is perpendicular to the field at t=0t=0.
Intuitive explanation

The key is recognizing that emf depends on how fast magnetic flux through the coil is changing. As the coil rotates, the angle between its normal and the field direction changes continuously, so the flux Φ=NBAcos⁡(θ)\Phi = NBA\cos(\theta) oscillates. The instantaneous emf is the negative rate of change of this flux—take the derivative with respect to time, and the cos⁡\cos term becomes a sin⁡\sin term with maximum amplitude NBAωNBA\omega.

Intuitive explanation

The key is recognizing that emf depends on how fast magnetic flux through the coil is changing. As the coil rotates, the angle between its normal and the field direction changes continuously, so the flux Φ=NBAcos⁡(θ)\Phi = NBA\cos(\theta) oscillates. The instantaneous emf is the negative rate of change of this flux—take the derivative with respect to time, and the cos⁡\cos term becomes a sin⁡\sin term with maximum amplitude NBAωNBA\omega.

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